High-performance computing and modern numerical algorithms have made high-fidelity fluid-thermal analysis tractable in geometries of ever increasing complexity. Despite continued advances in these areas, direct numerical (DNS), large eddy simulation (LES), and even unsteady Reynolds-averaged Navier-Stokes (URANS) simulations of turbulent thermal transport remain too costly for routine analysis and design of thermal-hydraulic systems, where hundreds of cases must be considered. Reduced order models (ROMs) offer a promising alternative by leveraging expensive high-fidelity simulations (referred to as full order models or FOMs) to first extract a low-dimensional basis that captures the principal features of the underlying flow fields, and then construct computational models whose dimensions are orders of magnitude lower than the FOM dimension. In the numerical simulation of fluid flows, Galerkin ROMs (G-ROMs), which use data-driven basis functions in a Galerkin framework, have provided efficient and accurate approximations of laminar flows, such as the two-dimensional flow past a circular cylinder at low Reynolds numbers [1, 2]. However, turbulent flows are notoriously hard for the standard G-ROM. Indeed, to capture the complex dynamics, a large number [3] of ROM basis functions is required, which yields high-dimensional ROMs that cannot be used in realistic applications. Thus, computationally efficient, low-dimensional ROMs are used instead. Unfortunately, these ROMs are inaccurate since the ROM basis functions that were not used to build the G-ROM have an important role in dissipating the energy from the system [4].

Solving complex planning problems requires Large Language Models (LLMs) to explicitly model the state transition to avoid rule violations, comply with constraints, and ensure optimality-a task hindered by the inherent ambiguity of natural language. To overcome such ambiguity, Planning Domain Definition Language (PDDL) is leveraged as a planning abstraction that enables precise and formal state descriptions. With PDDL, we can generate a symbolic world model where classic searching algorithms, such as A*, can be seamlessly applied to find optimal plans. However, directly generating PDDL domains with current LLMs remains an open challenge due to the lack of PDDL training data. To address this challenge, we propose to scale up the test-time computation of LLMs to enhance their PDDL reasoning capabilities, thereby enabling the generation of high-quality PDDL domains. Specifically, we introduce a simple yet effective algorithm, which first employs a Best-of-N sampling approach to improve the quality of the initial solution and then refines the solution in a fine-grained manner with verbalized machine learning. Our method outperforms o1-mini by a considerable margin in the generation of PDDL domain, achieving over 50% success rate on two tasks (i.e., generating PDDL domains from natural language description or PDDL problems). This is done without requiring additional training. By taking advantage of PDDL as state abstraction, our method is able to outperform current state-of-the-art methods on almost all competition-level planning tasks.

Nature is pervaded with oscillatory behavior. In networks of coupled oscillators patterns can arise when the system synchronizes to an external input. Hence, these networks provide processing and memory of input. We present a universal framework for harnessing oscillator networks as computational resource. This reservoir computing framework is introduced by the ubiquitous model for phase-locking, the Kuramoto model. We force the Kuramoto model by a nonlinear target-system, then after substituting the target-system with a trained feedback-loop it emulates the target-system. Our results are two-fold. Firstly, the trained network inherits performance properties of the Kuramoto model, where all-to-all coupling is performed in linear time with respect to the number of nodes and parameters for synchronization are abundant. Secondly, the learning capabilities of the oscillator network can be explained using Kuramoto model's order parameter. This work provides the foundation for utilizing nature's oscillator networks as a new class of information processing systems.

Connected and Automated Vehicle (CAV) research has gained traction in the last decade due to significant advancements in perception, navigation, communication, and control functions. Accurate and reliable position information is needed to meet the requirements of CAV applications, especially when safety is concerned. With the advent of various perception sensors (e.g. camera, LiDAR, etc.), the vehicular positioning system has improved both in accuracy and robustness. Vehicle-to-Vehicle (V2V) and Vehicle-to-Infrastructure (V2I) based cooperative positioning can improve the accuracy of the position estimates, but the integrity risks involved in multi-sensor fusion in a cooperative environment have not yet been fully explored. This paper reviews existing research in the field of positioning Integrity Monitoring (IM) and identifies various research gaps. Particular attention has been placed on identifying research that highlights cooperative IM methods. This analysis helps pave the way for the development of new IM frameworks for cooperative positioning solutions in the future.

This study introduces a hybrid machine learning-based scale-bridging framework for predicting the permeability of fibrous textile structures. By addressing the computational challenges inherent to multiscale modeling, the proposed approach evaluates the efficiency and accuracy of different scale-bridging methodologies combining traditional surrogate models and even integrating physics-informed neural networks (PINNs) with numerical solvers, enabling accurate permeability predictions across micro- and mesoscales. Four methodologies were evaluated: Single Scale Method (SSM), Simple Upscaling Method (SUM), Scale-Bridging Method (SBM), and Fully Resolved Model (FRM). SSM, the simplest method, neglects microscale permeability and exhibited permeability values deviating by up to 150\% of the FRM model, which was taken as ground truth at an equivalent lower fiber volume content. SUM improved predictions by considering uniform microscale permeability, yielding closer values under similar conditions, but still lacked structural variability. The SBM method, incorporating segment-based microscale permeability assignments, showed significant enhancements, achieving almost equivalent values while maintaining computational efficiency and modeling runtimes of ~45 minutes per simulation. In contrast, FRM, which provides the highest fidelity by fully resolving microscale and mesoscale geometries, required up to 270 times more computational time than SSM, with model files exceeding 300 GB. Additionally, a hybrid dual-scale solver incorporating PINNs has been developed and shows the potential to overcome generalization errors and the problem of data scarcity of the data-driven surrogate approaches. The hybrid framework advances permeability modelling by balancing computational cost and prediction reliability, laying the foundation for further applications in fibrous composite manufacturing.

The twenty-first century is a data-driven era where human activities and behavior, physical phenomena, scientific discoveries, technology advancements, and almost everything that happens in the world resulting in massive generation, collection, and utilization of data. Connectivity in data is a crucial property. A straightforward example is the World Wide Web, where every webpage is connected to other web pages through hyperlinks, providing a form of directed connectivity. Combinatorial data refers to combinations of data items based on certain connectivity rules. Other forms of combinatorial data include social networks, meshes, community clusters, set systems, and molecules. This Ph.D. dissertation focuses on learning and computing with combinatorial data. We study and examine topological and connectivity features within and across connected data to improve the performance of learning and achieve high algorithmic efficiency.

Artificial intelligence commonly refers to the science and engineering of artificial systems that can carry out tasks generally associated with requiring aspects of human intelligence, such as playing games, translating languages, and driving cars. In recent years, there have been exciting advances in learning-based, data-driven approaches towards AI, and machine learning and deep learning have enabled computer systems to perceive the world in unprecedented ways. Reinforcement learning has enabled breakthroughs in complex games such as Go and challenging robotics tasks such as quadrupedal locomotion. A key aspect of intelligence is to not only make predictions, but reason about the uncertainty in these predictions, and to consider this uncertainty when making decisions. This is what this manuscript on "Probabilistic Artificial Intelligence" is about. The first part covers probabilistic approaches to machine learning. We discuss the differentiation between "epistemic" uncertainty due to lack of data and "aleatoric" uncertainty, which is irreducible and stems, e.g., from noisy observations and outcomes. We discuss concrete approaches towards probabilistic inference and modern approaches to efficient approximate inference. The second part of the manuscript is about taking uncertainty into account in sequential decision tasks. We consider active learning and Bayesian optimization -- approaches that collect data by proposing experiments that are informative for reducing the epistemic uncertainty. We then consider reinforcement learning and modern deep RL approaches that use neural network function approximation. We close by discussing modern approaches in model-based RL, which harness epistemic and aleatoric uncertainty to guide exploration, while also reasoning about safety.

The attention mechanism was originally introduced in the context of large language models to learn relations between words [26]. Solving the many-electron Schrödinger equation for Here, the attention mechanism is employed to identify solids is an exceedingly difficult problem due to the exponential and quantify how electrons influence each other and how growth of the Hilbert space dimension. Various such influence affects their individual orbitals. This enable techniques based on the variational principle have long the construction of NN wavefunctions from Slater been developed to approximate the ground state of interacting determinants of generalized orbitals that depend on the electron systems using trial wavefunctions.

A generative AI architecture called bubbly flow generative adversarial networks (BF-GAN) is developed, designed to generate realistic and high-quality bubbly flow images through physically conditioned inputs, jg and jf. Initially, 52 sets of bubbly flow experiments under varying conditions are conducted to collect 140,000 bubbly flow images with physical labels of jg and jf for training data. A multi-scale loss function is then developed, incorporating mismatch loss and pixel loss to enhance the generative performance of BF-GAN further. Regarding evaluative metrics of generative AI, the BF-GAN has surpassed conventional GAN. Physically, key parameters of bubbly flow generated by BF-GAN are extracted and compared with measurement values and empirical correlations, validating BF-GAN's generative performance. The comparative analysis demonstrate that the BF-GAN can generate realistic and high-quality bubbly flow images with any given jg and jf within the research scope. BF-GAN offers a generative AI solution for two-phase flow research, substantially lowering the time and cost required to obtain high-quality data. In addition, it can function as a benchmark dataset generator for bubbly flow detection and segmentation algorithms, enhancing overall productivity in this research domain. The BF-GAN model is available online (https://github.com/zhouzhouwen/BF-GAN).

Estimation and inference for the Average Treatment Effect (ATE) is a cornerstone of causal inference and often serves as the foundation for developing procedures for more complicated settings. Although traditionally analyzed in a batch setting, recent advances in martingale theory have paved the way for adaptive methods that can enhance the power of downstream inference. Despite these advances, progress in understanding and developing adaptive algorithms remains in its early stages. Existing work either focus on asymptotic analyses that overlook exploration-exploitation tradeoffs relevant in finite-sample regimes or rely on simpler but suboptimal estimators. In this work, we address these limitations by studying adaptive sampling procedures that take advantage of the asymptotically optimal Augmented Inverse Probability Weighting (AIPW) estimator. Our analysis uncovers challenges obscured by asymptotic approaches and introduces a novel algorithmic design principle reminiscent of optimism in multiarmed bandits. This principled approach enables our algorithm to achieve significant theoretical and empirical gains compared to prior methods. Our findings mark a step forward in advancing adaptive causal inference methods in theory and practice.